The CUPID-Mo experiment to search for 0$ u\beta\beta$ decay in $^{100}$Mo has been recently completed after about 1.5 years of operation at Laboratoire Souterrain de Modane (France). It served as a demonstrator for CUPID, a next generation 0$ u\beta\beta$ decay experiment. CUPID-Mo was comprised of 20 enriched Li$_2$$^{100}$MoO$_4$ scintillating calorimeters, each with a mass of $\sim$ 0.2 kg, operated at $\sim$20 mK. We present here the final analysis with the full exposure of CUPID-Mo ($^{100}$Mo exposure of 1.47 kg$\times$yr) used to search for lepton number violation via 0$ u\beta\beta$ decay. We report on various analysis improvements since the previous result on a subset of data, reprocessing all data with these new techniques. We observe zero events in the region of interest and set a new limit on the $^{100}$Mo 0$ u\beta\beta$ decay half-life of $T^{0 u}_{1/2} > 1.8 \times 10^{24}$ year (stat.+syst.) at 90% CI. Under the light Majorana neutrino exchange mechanism this corresponds to an effective Majorana neutrino mass of $\left < (0.28$--$0.49)$ eV, dependent upon the nuclear matrix element utilized.

Precise characterization of detector time resolution is of crucial importance for next-generation cryogenic-bolometer experiments searching for neutrinoless double-beta decay, such as CUPID, in order to reject background due to pile-up of two-neutrino double-beta decay events. In this paper, we describe a technique developed to study the pile-up rejection capability of cryogenic bolometers. Our approach, which consists of producing controlled pile-up events with a programmable waveform generator, has the benefit that we can reliably and reproducibly control the time separation and relative energy of the individual components of the generated pile-up events. The resulting data allow us to optimize and benchmark analysis strategies to discriminate between individual and pile-up pulses. We describe a test of this technique performed with a small array of detectors at the Laboratori Nazionali del Gran Sasso, in Italy; we obtain a 90% rejection efficiency against pulser-generated pile-up events with rise time of ~15ms down to time separation between the individual events of about 2ms.

CUPID will be a next generation experiment searching for the neutrinoless double $\beta$ decay, whose discovery would establish the Majorana nature of the neutrino. Based on the experience achieved with the CUORE experiment, presently taking data at LNGS, CUPID aims to reach a background free environment by means of scintillating Li$_{2}$$^{100}$MoO$_4$ crystals coupled to light detectors. Indeed, the simultaneous heat and light detection allows us to reject the dominant background of $\alpha$ particles, as proven by the CUPID-0 and CUPID-Mo demonstrators. In this work we present the results of the first test of the CUPID baseline module. In particular, we propose a new optimized detector structure and light sensors design to enhance the engineering and the light collection, respectively. We characterized the heat detectors, achieving an energy resolution of (5.9 $\pm$ 0.2) keV FWHM at the $Q$-value of $^{100}$Mo (about 3034 keV). We studied the light collection of the baseline CUPID design with respect to an alternative configuration which features gravity-assisted light detectors' mounting. In both cases we obtained an improvement in the light collection with respect to past measures and we validated the particle identification capability of the detector, which ensures an $\alpha$ particle rejection higher than 99.9%, fully satisfying the requirements for CUPID.